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One edge of a square plate with insulated faces is kept at a uniform temperature u0,...

One edge of a square plate with insulated faces is kept at a uniform temperature u0, and the other three edges are kept at temperature zero. Without solving a boundary value problem, but by superposition of like problems to obtain the trivial case in which all four edges are at temperature u0, show why the steady temperature at the center of the given plate must be u0/4.

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